Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fatih Kızılaslan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Design Methodology ◽  
Parallel Systems ◽  
Parallel System ◽  
Series System ◽  
Stochastic Comparisons ◽  
Content Type ◽  
Reversed Hazard Rate ◽  
The Relationship

PurposeThe purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.Design/methodology/approachThe obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.FindingsThe reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.Originality/valueTo the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications

2020 ◽  
Vol 57 (3) ◽  
pp. 832-852
Author(s):  
Lu Li ◽  
Qinyu Wu ◽  
Tiantian Mao
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Parallel Systems ◽  
Rate Model ◽  
Stochastic Comparisons ◽  
Reversed Hazard Rate ◽  
Generalized Gamma ◽  
Pareto Distributions ◽  
Hazard Rate Model

AbstractWe investigate stochastic comparisons of parallel systems (corresponding to the largest-order statistics) with respect to the reversed hazard rate and likelihood ratio orders for the proportional reversed hazard rate (PRHR) model. As applications of the main results, we obtain the equivalent characterizations of stochastic comparisons with respect to the reversed hazard rate and likelihood rate orders for the exponentiated generalized gamma and exponentiated Pareto distributions. Our results recover and strengthen some recent results in the literature.

COMPARISONS OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

2013 ◽  
Vol 28 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Weiyong Ding ◽  
Gaofeng Da ◽  
Xiaohu Li
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Parallel Systems ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Series Systems

This paper carries out stochastic comparisons of series and parallel systems with independent and heterogeneous components in the sense of the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. The main results extend and strengthen the corresponding ones by Misra and Misra [18] and by Ding, Zhang, and Zhao [8]. Meanwhile, the results on the hazard rate order of parallel systems and the reversed hazard order of series systems serve as nice supplements to Theorem 16.B.1 of Boland and Proschan [4] and Theorem 3.2 of Nanda and Shaked [20], respectively.

scholarly journals Stochastic Order Relations Among Parallel Systems from Weibull Distributions

2015 ◽  
Vol 52 (01) ◽  
pp. 102-116 ◽  
Author(s):  
Nuria Torrado ◽  
Subhash C. Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Variables ◽  
Parallel Systems ◽  
Parallel System ◽  
Weibull Distributions ◽  
Scale Parameters ◽  
Order Relations ◽  
Stochastic Order Relations

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

STOCHASTIC COMPARISONS OF LARGEST ORDER STATISTICS FROM MULTIPLE-OUTLIER EXPONENTIAL MODELS

2012 ◽  
Vol 26 (2) ◽  
pp. 159-182 ◽  
Author(s):  
Peng Zhao ◽  
N. Balakrishnan
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Exponential Models ◽  
Usual Stochastic Order

In this paper, we carry out stochastic comparisons of largest order statistics from multiple-outlier exponential models according to the likelihood ratio order (reversed hazard rate order) and the hazard rate order (usual stochastic order). It is proved, among others, that the weak majorization order between the two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between largest order statistics, and that the p-larger order between the two hazard rate vectors is equivalent to the hazard rate order (usual stochastic order) between largest order statistics. We also extend these results to the proportional hazard rate models. The results established here strengthen and generalize some of the results known in the literature.

scholarly journals Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 856
Author(s):  
Narayanaswamy Balakrishnan ◽  
Ghobad Barmalzan ◽  
Sajad Kosari
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Parallel Systems ◽  
Hazard Rates ◽  
Stochastic Comparisons ◽  
Reversed Hazard Rate ◽  
Usual Stochastic Order ◽  
Distributed Components

In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples.

scholarly journals Stochastic Order Relations Among Parallel Systems from Weibull Distributions

2015 ◽  
Vol 52 (1) ◽  
pp. 102-116 ◽  
Author(s):  
Nuria Torrado ◽  
Subhash C. Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Variables ◽  
Parallel Systems ◽  
Parallel System ◽  
Weibull Distributions ◽  
Scale Parameters ◽  
Order Relations ◽  
Stochastic Order Relations

Let Xλ1, Xλ2, …, Xλn be independent Weibull random variables with Xλi ∼ W(α, λi), where λi > 0 for i = 1, …, n. Let Xn:nλ denote the lifetime of the parallel system formed from Xλ1, Xλ2, …, Xλn. We investigate the effect of the changes in the scale parameters (λ1, …, λn) on the magnitude of Xn:nλ according to reverse hazard rate and likelihood ratio orderings.

scholarly journals Stochastic Order Relations Among Parallel Systems from Weibull Distributions

2015 ◽  
Vol 52 (01) ◽  
pp. 102-116
Author(s):  
Nuria Torrado ◽  
Subhash C. Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Variables ◽  
Parallel Systems ◽  
Parallel System ◽  
Weibull Distributions ◽  
Scale Parameters ◽  
Order Relations ◽  
Stochastic Order Relations

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

Perceptions of time at work

2016 ◽  
Vol 45 (1) ◽  
pp. 29-50 ◽  
Author(s):  
Aristides Isidoro Ferreira ◽  
Joana Diniz Esteves
Keyword(s):  
Gender Differences ◽  
Design Methodology ◽  
Internet Use ◽  
The Internet ◽  
Content Type ◽  
Future Studies ◽  
Work Related ◽  
Phone Calls ◽  
Working Day ◽  
The Relationship

Purpose – Activities such as making personal phone calls, surfing on the internet, booking personal appointments or chatting with colleagues may or may not deviate attentions from work. With this in mind, the purpose of this paper is to examine gender differences and motivations behind personal activities employees do at work, as well as individuals’ perception of the time they spend doing these activities. Design/methodology/approach – Data were obtained from 35 individuals (M age=37.06 years; SD=7.80) from a Portuguese information technology company through an ethnographic method including a five-day non-participant direct observation (n=175 observations) and a questionnaire with open-ended questions. Findings – Results revealed that during a five-working-day period of eight hours per day, individuals spent around 58 minutes doing personal activities. During this time, individuals engaged mainly in socializing through conversation, internet use, smoking and taking coffee breaks. Results revealed that employees did not perceive the time they spent on non-work realted activities accurately, as the values of these perceptions were lower than the actual time. Moreover, through HLM, the findings showed that the time spent on conversation and internet use was moderated by the relationship between gender and the leisure vs home-related motivations associated with each personal activity developed at work. Originality/value – This study contributes to the literature on human resource management because it reveals how employees often perceive the time they spend on non-work related activities performed at work inaccurately. This study highlights the importance of including individual motivations when studying gender differences and personal activities performed at work. The current research discusses implications for practitioners and outlines suggestions for future studies.

Learning from intelligent conversation

IMP Journal ◽  
2016 ◽  
Vol 10 (3) ◽  
pp. 512-539 ◽  
Author(s):  
Luitzen De Boer ◽  
Poul Houman Andersen
Keyword(s):  
System Theory ◽  
Design Methodology ◽  
Historical Analysis ◽  
Research Field ◽  
Literature Study ◽  
Content Type ◽  
Narrative Literature ◽  
The Relationship ◽  
Conceptual Research

Purpose The purpose of the paper is to contribute to further advancing of IMP as a research field by setting up and starting a theoretical conversation between system theory and the IMP. Design/methodology/approach The approach is based on a narrative literature study and conceptual research. Findings The authors find that system theory and cybernetics can be regarded as important sources of inspiration for early IMP research. The authors identify three specific theoretical “puzzles” in system theory that may serve as useful topics for discussion between system theorists and IMP researchers. Originality/value Only a handful of papers have touched upon the relationship between system theory and IMP before. This paper combines a narrative, historical analysis of this relationship with developing specific suggestions for using system theory as a vehicle for further advancement of IMP research.

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